Determination of all groups of order 2^m which contain cyclic self-conjugate sub-groups of order 2^(m-4) and whose generating operations correspond to the partitions (m-4,4), (m-4,3,1)

Determination of all groups of order 2^m which contain cyclic self-conjugate sub-groups of order 2^(m-4) and whose generating operations correspond to the partitions (m-4,4), (m-4,3,1)